This document provides diagnostic plots for several spawner-recruit models that were used to characterize Canadian-origin Yukon Chinook salmon population dynamics at the Conservation Unit scale as described in:

Connors, B.M., O’Dell, A., Hunter, H., Glaser, D., Gill, J., Rossi, S., and Churchland, C. 2025. Stock status and biological and fishery consequences of alternative harvest and rebuilding actions for Yukon River Chinook salmon (Oncorhynchus tshawytscha). DFO Can. Sci. Advis. Sec. Res. Doc. 2025/nnn. iv + 107 p.

Full details are provided in the document above but briefly, four state-space spawner-recruit models were fit: spawer-recruitment models with autoregressive recruitment residuals (labelled “AR1”), (2) spawner-recruitment models with time varying intrinsic productivity (labelled “TV”), and (3) egg mass-recruitment models with AR1 recruitment residuals (labelled “AR1 egg mass”). These models were fit to each of the nine Conservation Units for which we had data.

Diagnostics

We fit the spawner-recruitment model in a Bayesian estimation framework with Stan (Carpenter et al. 2017; Stan Development Team 2023), which implements the No-U-Turn Hamiltonian Markov chain Monte Carlo algorithm (Hoffman and Gelman 2014)) for Bayesian statistical inference to generate a joint posterior probability distribution of all unknowns in the model. The models can be found here.We sampled from 4 chains with 4,000 iterations each and discarded the first half as warm-up. We assessed chain convergence visually via trace plots and by ensuring that \(\hat{R}\) (potential scale reduction factor; Vehtari et al. 2021) was less than 1.1 and that the effective sample size was greater than 400. Posterior predictive checks were used to make sure the model returned known values, by simulating new datasets and checking how similar they were to our observed data.

Trace plots

These should be clearly mixed, with no single distribution deviating substantially from others (left column), and no chains exploring a strange space for a few iterations (right column). “D_scale” is the \(D\) term in equation C.4 in the research document and governs variability of age proportion vectors across cohorts.”Dir_alpha” refers to Dirichlet shape parameter for the gamma distribution used to generate vector of age-at-maturity proportions.

Big.Salmon

MiddleYukonR.andtribs.

Nordenskiold

NorthernYukonR.andtribs.

Pelly

Stewart

UpperYukonR.

Whiteandtribs.

YukonR.Teslinheadwaters

ESS and \(\hat{R}\)

We aimed for minimum effective sample sizes that are greater than 400 and \(\hat{R}\) values less than 1.1.The tables below summarize the lowest effective sample size (ESS) and largest \(\hat{R}\) across all estimated parameters for each CU and class of model.

AR1 model:

CU ESS Rhat
Big.Salmon 109 1.055
MiddleYukonR.andtribs. 302 1.009
Nordenskiold 822 1.004
NorthernYukonR.andtribs. 331 1.003
Pelly 140 1.046
Stewart 262 1.013
UpperYukonR. 319 1.039
Whiteandtribs. 240 1.013
YukonR.Teslinheadwaters 250 1.014

Time varying (TV) model:

CU ESS Rhat
Big.Salmon 127 1.032
MiddleYukonR.andtribs. 152 1.041
Nordenskiold 447 1.011
NorthernYukonR.andtribs. 224 1.013
Pelly 152 1.022
Stewart 160 1.016
UpperYukonR. 355 1.014
Whiteandtribs. 270 1.015
YukonR.Teslinheadwaters 156 1.019

Egg mass AR1 model:

CU ESS Rhat
Big.Salmon 123 1.026
MiddleYukonR.andtribs. 149 1.005
Nordenskiold 614 1.005
NorthernYukonR.andtribs. 255 1.015
Pelly 148 1.027
Stewart 162 1.050
UpperYukonR. 286 1.009
Whiteandtribs. 194 1.017
YukonR.Teslinheadwaters 182 1.022